We study the behaviour of the Lorentzian Engle-Pereira-Rovelli-Livine
    spinfoam amplitude with homogeneous boundary data, under a graph refinement
    going from five to twenty boundary tetrahedra. This can be interpreted as a
    wave function of the universe, for which we compute boundary geometrical
    operators, correlation functions and entanglement entropy. The numerical
    calculation is made possible by adapting the Metropolis-Hastings algorithm,
    along with recently developed computational methods appropriate for the deep
    quantum regime. We confirm that the transition amplitudes are stable against
    such refinement. We find that the average boundary geometry does not change,
    but the new degrees of freedom correct the quantum fluctuations of the boundary
    and the correlations between spatial patches. The expectation values are
    compatible with their geometrical interpretation and the correlations between
    neighbouring patches decay when computed across different spinfoam vertices.

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